To take a simple example, consider a case in which the parties agree on damages and dispute only liability. Let L denote the damages that the defendant would pay the plaintiff if the court were to find liability. Let p denote the probability that the plaintiff prevails on liability, with 0 < p < 1. Thus, the distribution features a discrete probability mass of p at D = L and a discrete probability mass of 1-p at D = 0. In this example, D = pL, and Pr(D < D) = 1-p. In this case, Proposition 7 implies the following:
Corollary: If a one-party offer-of-settlement rule with two-sided cost-shifting requires a party to mate a special offer, and the parties dispute only liability, then:
(a) If p < V2, then the settlement amount will be S* < D. (b) Ifp > Vi, then the settlement amount will be S* > D.
Finally, by the same reasoning used to prove Proposition 6, we can also show that the same outcomes would emerge under a two-party offer-of-settlement rule. In particular, if both parties can mate a special offer, settlement will always occur at the same S*, because each party could ensure an outcome at least that favorable for itself by making a special offer. Therefore, both Proposition 7 and its corollary would apply under any two-party rule.
IMPLICATIONS FOR OUTCOMES UNDER THE EXISTING RULE 68
Our analysis enables us to identify the outcome under any given offer-of-settlement rule. To illustrate, let us now apply this analysis to the outcomes expected under the existing Rule 68. As noted, under Rule 68 as it currently stands, only the defendant has the option of making a special offer, and such an offer can trigger only one-sided cost-shifting.
Assume for a moment that if the plaintiff obtains less at trial than the special offer, the defendant would always get full reimbursement for all litigation costs. Under this assumption, the settlement amount would be the S* that solves equation (5):